嘎逼居熊熊 10 Posted May 20, 2005 Report Share Posted May 20, 2005 這是我們學校國中部數學有獎徵答的題目個人覺得蠻難的大家挑戰看看吧---------------------------------------------------在 7/25 與 25/89 之間的分數中分母最小的是?? Link to post Share on other sites
一切從零開始 10 Posted May 20, 2005 Report Share Posted May 20, 2005 最初由 咖啡中毒者 發表---------------------------------------------------在 7/25 與 25/89 之間的分數中分母最小的是?? 我猜16/57 Link to post Share on other sites
江湖舊夢 10 Posted May 20, 2005 Report Share Posted May 20, 2005 7/25 = 623/(25*89)25/89 = 625/(89*25)介於兩數之間的只有624/(25*89)∵624與(25*89)互值∴最小分母為25*89 = 2225 Link to post Share on other sites
源良 10 Posted August 26, 2008 Report Share Posted August 26, 2008 沒可能2225吧,你可以驗驗看, 一切從零開始 所給的16/57已經在兩個分數之間了.除了編個程式讓電腦做,或自己由1/2,1/3,2/3,1/4,2/4,3/4...一直試外,我想不到任何方法做了. Link to post Share on other sites
newaccXD 10 Posted August 26, 2008 Report Share Posted August 26, 2008 設所求分數為A/B(A,B皆屬於N)7B<25A 且 89A<25B令7B+K=25A , 89A+T=25B已知A,B屬於N,故K,T也屬於N兩式聯立:623B+89K=625B-25T2B=89K+25TK,T皆為自然數故B最小值為57,此時K=T=1 Link to post Share on other sites
黑夜星羽 10 Posted September 13, 2008 Report Share Posted September 13, 2008 個人認為是5= = Link to post Share on other sites
YCLin 10 Posted September 21, 2008 Report Share Posted September 21, 2008 9 Link to post Share on other sites
chiajung 10 Posted May 3, 2009 Report Share Posted May 3, 2009 7/25 = 623/(25*89)25/89 = 625/(89*25)介於兩數之間的只有624/(25*89)∵624與(25*89)互值∴最小分母為25*89 = 2225我同意這個想法耶 Link to post Share on other sites
愛力克斯 10 Posted May 3, 2009 Report Share Posted May 3, 2009 確認一下 分數的分母跟分子不一定要是整數吧? Link to post Share on other sites
聽說我叫便當 10 Posted May 3, 2009 Report Share Posted May 3, 2009 我同意這個想法耶同意+1..不過按了按計算機16/57真的在兩數中間 Link to post Share on other sites
路人囧 10 Posted May 8, 2009 Report Share Posted May 8, 2009 7/25 = 623/(25*89)25/89 = 625/(89*25)介於兩數之間的只有624/(25*89)∵624與(25*89)互值∴最小分母為25*89 = 2225介於623、625這兩數之間不是只有624還要考慮小數例如： 624.78/(25×89)= 62478/(25×89×100)= 702/(25×100)= 351/(25×50)25×50=1250（小於2225）至於最小值……我認為是無限小因為題目沒說分子、分母不能為負數=ˇ=（被巴）如果分子、分母可為無理數的話在下就不知該如何解了……orz限定為正整數的話，那就照5樓大大的算法得出其值為16/57 Link to post Share on other sites
eros0828 10 Posted May 9, 2009 Report Share Posted May 9, 2009 分母最小??分數最小??糟糕~我看不懂題目= ="為什麼會出現2225~也太大~?? Link to post Share on other sites
OldxLeo 10 Posted July 20, 2009 Report Share Posted July 20, 2009 分母最小??分數最小??糟糕~我看不懂題目= ="為什麼會出現2225~也太大~??在 7/25 與 25/89 之間的分數中7~~~~2525~~~89分母最小的是??在這之間有很多 分數找出在這所有的分數裡面分母最小的那一個(整個分數要大於7/25 小於25/89出現2225的原因是江湖前輩先擴分而不是用不等式的式子去討論不知道是不是這樣? Link to post Share on other sites
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